Consider the curve defined by t and y = 2t² +6, for -2 ≤ t ≤ 3. Find an equation in x and y whose graph includes the graph of the given curv y = 4x² + 6 y = x² +6 = 8x² +6 X = O y = O y = 2x² + 8

Q: b. Enclosed by the curves y² = 4x + 4 and the line y = 4x – 16.

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Q: 2. Find y in terms of x if = 6x² – 2x and the curve passes through the point (1, 5). -

A: We have to find the value of x if dydx=6x2-2x and the curve passes through the point (1,5).…

Q: Describe the curve generated by x = 3 + 2t, y = -12 - 6t, for - ∞ < t < ∞.

A: Given: x=3+2t y=-12-6t            - ∞ < t < ∞ To find: curve generated by given functions.

Q: 11) Find each of the two areas bounded by the curves y=x3-4x and y=x² + 2x Points of intersection:…

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Q: Find the length of the following curve. y = 2x + 4 on 3-2, 24 (Use calculus.)

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Q: Identify and sketch the curve for x2-y2-6x = 0

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Q: Graph the relation of equation x2/4 + y2/16 = 1 using the points calculated in the table below.…

A: Answer

Q: 9). Find the curve whose slope at any point is 3x – 5 that passes through point (5,3).

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Q: 1.) y = 2 X²+1

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: The point (0, 1) has the distance from the line defined by y = -2x – 1

A: Solve for distance

Q: Find the set of values of y=2x+k meets the curve y=1+2kx-x² at 2 distinct points?

A: Given: y=2x+kat 2 distinct points

Q: Find the length of the curve: - for 1< y<3. 3 4y 4. x=

A: As we know that the length of a curve x=f(y) is given by:- L=∫ab(f'(y))2+1dy

Q: Find the point on the curve y = √x closest to the point (2,2)

A: Here we have to find the point on the curve y = sqrt (x) closest to the point (2, 2)   use the…

Q: Show that the distance between the line 3x 4y + 3 = 0 and the point (1, –1) is 2. |

A: In this question, we have to prove that the distance between line and point is 2.

Q: Consider the curve defined by x = 2t – 1 and Y = 2 – t, for –5 <t< 3. Find an equation in X and Y…

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